I am just learning bitcoin and am confused on two issues.
What prevents one miner (Miner A) from creating a block including transaction X which has a transaction fee associated with it, and Miner B working on a separate block which also has the same transaction X in it. Clearly both of them cannot get the transaction fee. Does whoever solves it first get the bitcoins, and the loser gets nothing? Or are transactions "claimed" when you create a block, so others cannot also work on verifying them.
Is it possible for somebody to not have their transaction be verified in a long time? What if no miner picks up their transaction in their respective block they are working on? Or are the chances of that very low.